The Physical Layer

We are interested in transmission media, how data is transmitted over them, and the communications systems that use them.

Some basic concepts

One thing all transmission media have in common is that data is transmitted on waves.  So we need to consider some of the physical properties of waves.

Fourier series

Waves are periodic functions.  Every periodic function can be expressed as a Fourier series, which is an infinite series whose terms are sine and cosine functions.  Each term of a Fourier series is a sine or cosine function of a different frequency; each frequency is an integral multiple of the fundamental frequency.



The decomposition is unique.  That is, given a periodic function f, the coefficients a_n and b_n which comprise the Fourier series can be determined uniquely.  Likewise, the function f can be reconstructed if the Fourier coefficients are known.

==>  Something fundamental is going on here.  A signal on a wire (or some other medium) is really a bundle of signals at different frequencies.

One implication has to do with the difference between digital and analog signals. 

Suppose we want to send a series of bits, with 0's and 1's represented by two different voltage levels, as we might find on the wires within a CPU.





This waveform has a representation as a Fourier series.  That is, it can be decomposed into a sum of sine and cosine waves.  However,  the a_n and b_n coefficients don't tend to 0 quickly.  Many terms are needed to give a good approximation to the actual signal.  A wide spectrum is required.

This causes problems when transmitting over any real medium.

• Voice-grade telephone lines do not transmit signals above 3000 mHz.  (The range is about 300 - 3000 mHz)  So much of the signal is filtered out.  The result is that only an approximation of the original signal is transmitted and received.
• Over long distances, different frequencies have different characteristics with respect to attenuation (signal fade due to loss of energy) and delay distortion (different speeds, so that some components may become out-of-phase with others).
• It would waste bandwidth.  One signal would need to use a wide range of frequencies.

Modulation

As a result, what is done is to have a continuous signal called a carrier at a certain frequency:

Data is then encoded by making small changes in the signal.  This is called modulation.  (as in AM = amplitude modulation and FM = frequency modulation radio)

Three types of modulation:

• Amplitude modulation
• susceptible to noise
• Frequency modulation
• two carriers -- requires more bandwidth
• Phase modulation
• skip a chunk of the wave
• permits more than one signal per band

Some terminology

• baud rate (or signal rate)  number of signal changes per second.  300 baud = 300 changes per second
• bit rate (or data rate)   number of bits per second
• bandwidth:  range of frequencies which can be transmitted -- measured in cycles per second

How are they related?

Changing the signal faster than two times the highest frequency does no good -- they will appear as higher frequency signals and filtered out.

Nyquist's theorem

Let H = bandwidth
Let V = number of discrete signal levels

The the maximum data rate = 2Hlog₂V bits per second

That's with no noise.  If channel is noisy, the maximum rate may be less.

Shannon's theorem

Let S/N = signal to noise ratio of a channel

The quantity 10 log₁₀ S/N is measured in decibels
If sig to noise ratio is 30 dB, then S/N = 10³ = 1000

Then maximum data rate = H log₂ (1 + S/N)

For telephone lines, that is

3000 * log₂ (1 + 1000) = 3000 * 10 = 30000 bps

According to Nyquist's theorem, the maximum data rate = 2 * 3000 log2 V = 6000 log2 V

To achieve higher data rates, a combination of amplitude modulation and phase-shift modulation can be used.  This is called Quadrature Amplitude Modulation (QAM).

Some examples:

1. The first modems used 300 baud.
• FSK - Frequency shift keying
• send:  1070 Hz = 0, 1270 Hz = 1
• receive:  2025 Hz = 0, 2225 Hz = 1
• data rate = baud rate = 300 bps
2. V.32bis
• 2400 baud
• 128-QAM   (128 = 2⁷, so this method achieved 7 bits per baud, with 1 bit used as a parity bit)
• data rate = 14400 bps
3. V.34
• 2400 baud
• data rate = 28800 bps
  
4. V.90
• upstream, same as V.34bis (33600 bps)
• downstream, all digital up to the subscriber-side local loop, capable of 56K bps
• no analog-to-digital on ISP side
• lower noise level

Transmission media:

• guided media
  
• wire
• twisted pair
• coaxial cable
• glass fiber
• unguided media
• wireless
• radio waves
• microwave
• infrared
• satellite

Copper wire

Copper wire is the most common transmission medium.

• analog or digital
• used for lines between gates in a CPU chip
• bus lines in a computer
• LANs
• WANs

Requires a circuit between transmitter and receiver

The transmitter applies a voltage at its end; this results in an electrical current sent down the wire; it can be detected by the receiver at the other end.

One problem is interference.

A current in one wire generates an electromagnetic wave.  This can generate currents (signals) in other nearby wires.

Two solutions to the interference problem result in the two main types of wire used for data communications:  twisted pair and coaxial cable.

twisted pair

• Two wires are insulated and wrapped around each other.
• Twisted pair is used throughout the telephone system.

coaxial cable

• used by cable TV.
• provides better shielding from interference
  

Optical fiber (fiber optics)

Transmitter uses light emitting diode (LED) or laser to send light pulses (ILD - injection laser diode)
pulse = 1, no pulse = 0

light will bounce off edges and continue, reducing the need for repeaters
"total internal reflection"

Comparison with copper

• Advangtages
• Dramatically higher bandwidth ==> higher data rates
  
• Use infrared light in the range or around 10¹⁴ Hz
• Achievable bandwidth in excess of 50,000 Gbps
  
• Low attenuation (i.e., loss of power)
• Repeaters every 30 km (copper wire needs every 5 km)
• No electromagnetic interference, corrosion, power surges
• Lightweight
• Does not need a circuit
  
• Disadvantages
• New
• Lack of people with skill in working with fiber
• Higher maintenance costs
• Unidirectional
• More fragile

Fiber is used for

• Long-distance trunk lines in telephone system
• 20-60,000 voice channels
• Undersea cables
• Metropolitan trunks
• Rural exchange trunks
• Subscriber loops
• For business now, home later
• Local area networks

Unguided media

That is, wireless transmission

There are several forms:  Radio waves, microwave, infrared

• Radio waves (30 MHz - 1 GHz)
• like radio and TV broadcast
• can penetrate buildings
• travel long distances
• omnidirectional
• Microwave (2 - 40 GHz)
• higher frequency than radio waves
• unidirectional  - can be aimed
• long used for long-distance telephone networks
• do not bend with the curvature of the earth, so tall towers and repeaters are needed (line-of-sight)
• do not pass through buildings well
• used for long-haul telephone transmission
• Infrared
• higher frequency than microwave
• directional
• do not pass through solid objects
• used for small single-room networks or indoor wireless LANs

Satellite transmission

Microwaves can also use satellites for transmission

The satellite acts as a "transponder" - it receives signals, then retransmits them back to earth.  A "big repeater in the sky".

Two types of satellite:

Geosynchronous

• remains stationary above some point on earth
• must be at specific altitude, approximately 36000 km above the equator
• good for broadcast
• not good for security

Low-orbit

• only 200-400 miles up
• satellites move in orbit
• many satellites are needed to cover the earth
• at any given time, use the closest satellite

In comparison with fiber, satellite has much lower bandwidth, so it is limited to niche applications:

• bypass local loop with satellite dish
• mobile communication
• broadcast
• cellular radio
• cell phones